Asymmetric parameter enhancement in the split-ring cavity array for virus-like particle sensing

Quantitative detection of virus-like particles under a low concentration is of vital importance for early infection diagnosis and water pollution analysis. In this paper, a novel virus detection method is proposed using indirect polarization parametric imaging method combined with a plasmonic split-ring nanocavity array coated with an Au film and a quantitative algorithm is implemented based on the extended Laplace operator. The attachment of viruses to the split-ring cavity breaks the structural symmetry, and such asymmetry can be enhanced by depositing a thin gold film on the sample, which allows an asymmetrical plasmon mode with a large shift of resonance peak generated under transverse polarization. Correspondingly, the far-field scattering state distribution encoded by the attached virus exhibits a specific asymmetric pattern that is highly correlated to the structural feature of the virus. By utilizing the parametric image sinδ to collect information on the spatial photon state distribution and far-field asymmetry with a sub-wavelength resolution, the appearance of viruses can be detected. To further reduce the background noise and enhance the asymmetric signals, an extended Laplace operator method which divides the detection area into topological units and then calculates the asymmetric parameter is applied, enabling easier determination of virus appearance. Experimental results show that the developed method can provide a detection limit as low as 56 vp/150µL on a large scale, which has great potential in early virus screening and other applications.


Theory and calculation of PIMI
PIMI system [1] is a method to observe birefringence in samples and image indirect parameters at a large scale. Considering a birefringent position on the sample, the phase difference between fast axis and slow axis is Here L is light path and λ is wavelength, and the polarization ellipse orientation angle is defined as angle between fast axis and X axis. In PIMI system, a rotating polarizer with angle of is placed before the sample, with reflected light from the sample sequncingly go through a quarter wave plate and a 45˚ polarizer. The output Intensity are Where (the subscript i represents the number of polarization rotation angles) indicates the pixel intensity. 0 is the average intensity under all polarization states. represents the sine of the phase difference between two orthogonal polarization components. is the polarization angle of the linearly polarized incident beam and is the polarization ellipse orientation angle of the reflected beam from the sample. By expanding Eq. (S2) trigonometrically, it can be reformulated in the following form: With a total number of steps N = 180°/18°, a 0 , a 1 and a 2 can be calculated as: Thus, the PIMI parameters, sinδ and ϕ can be extracted by utilizing the above equations. II.

Diagram of PIMI system
Fig. S1. Diagram of measurement using the PIMI system.

Simulation and experimental results for different sample statuses
In the manuscript, several sample processing steps are proposed to enhance the asymmetric signal. The sample could be classified into these statuses: 1. A bare split-ring. 2. A split-ring attached with a virus. 3. A bare split-ring covered with an Au layer. 4. A split-ring attached with a virus and covered with an Au layer. The basic logic we tried to express in the manuscript could be simply conclude as follows in Fig. S3. A transverse mode is generated for a bare split-ring. When a virus is attached to the split-ring, as shown in Fig. S3 (b), barely any influences are generated to the transverse mode, which means a weak sensing ability. To enhance the asymmetry caused by the virus, a layer of Au is deposited. The basic transverse mode for the bare split-ring covered with the Au layer does not change. For the status 4, however, this mode cannot be held any more. Due to the physical connection of metal at the virus side, the mode symmetry is then strongly broken. In Fig. S3 (d), we could clearly recognize an asymmetry along the longitudinal direction, which represents the existence of the virus. The influences of this near-field physical mechanism would also be characterized at a certain height, where the electromagnetic waves propagate away from the metal surface and could be detected by the far-field techniques, i.e., the PIMI method mentioned in the manuscript. With a monitor set at the height of 100 nm from the top surface of the split-ring in the simulation, we could directly establish the connection between the near-field results and far-field polarization parameter images. The simulated sinδ results from Fig. S4(a) to (d) correspond to the near-field results from status 1 to status 4 in Fig. S3, respectively. For the bare split-ring, the transverse dipoles in the sinδ image connect with each other and form a strip, which indicates an asymmetry for near-field modes along X and Y direction. When a virus is attached, the sinδ pattern does not show too much mutation. The experimental results for these two statuses could match the simulation results with a transverse strip.
However, the sinδ pattern would alter to another form, where the longitudinal dipoles connect, rather than the transverse dipoles. This phenomenon is generated by interference between the scattering mode of the split-ring and the substrate reflection [2,3]. Under this theory, the far-field electric field distribution we can detect could be transferred into other patterns when the substrate changes, i.e., a Si substrate and an Au substrate. This variation of the sinδ pattern is also observed in the experimental results in Fig. S4 (a) and (c). At last, for a sample site at status 4, an obvious asymmetry is generated along longitudinal direction both in the simulation and the experiment, i.e. Fig. S4 (c) and (d), which reflects the near-field mode asymmetry caused by the virus-attachment similar as in Fig. S3 (c) and (d).
For all four processing statuses of the sample, the experimental sinδ results agree well with the corresponding simulation results. In fact, the simulated PIMI results in Fig. S4 and simulated electric field distributions in Fig. S3 are acquired at different heights in the same simulations. That means these results share the same reliability. Thus, we believe that the uniformity between PIMI results for simulations and experiments in Fig. S4 can prove the change of near-field mode distribution caused by the virus.